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Optimal Attitude Motions for Microspacecraft: Analytical & Pseudospectral Methods

Albert Caubet's research explores autonomous repointing for microspacecraft, using analytical and pseudospectral methods to optimize attitude motions. Discover analytical approaches, pseudospectral methods for optimal control, and future work for improving motion planning in space.

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Optimal Attitude Motions for Microspacecraft: Analytical & Pseudospectral Methods

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  1. Astronet School – Rome Early Research Presentation Optimal and Feasible Attitude Motions for Microspacecraft Albert Caubet

  2. Background • UniversitatPolitecnica de Catalunya (UPC) – Aeronautical Engineering (specialization space vehicles) • CNES (2011-2012) • Mission Rosetta: Lander’s descent trajectory optimization • Long-term orbit propagator for space debris treatment (French Space Act). Resonances due to tesseral terms; modelling • University of Strathclyde [Glasgow] – Marie‐Curie Early Stage Researcher within the AstroNet‐II Training Network – PhD (Oct 2012-2015) Albert Caubet

  3. Overview • Aim: • Explore new ways of autonomous repointing (on-board planner) for micro- and nano- spacecraft • Challenges: • Limited torque, RW quick saturation  Optimal motions • Low computational power available  Light algorithms • Area:Motion Planning Attitude Control Albert Caubet

  4. Outline of the work so far • Attitude system: Reaction Wheels in the 3 orthogonal axis • Current plan: 1) obtain an optimal trajectory, and 2) track it with a simple controller • Main idea: To use close-to-optimal analytical motions as a good initial guess for numerical optimizers – path planning algorithms • Analytical approaches: • Spin-stabilized S/C: derivation of a parametric reference motion using geometric control theory – unconstrained parameter optimization (Dr. Biggs) • Free motions of axisymmetric and asymmetric spacecraft (Pagnozzi & Maclean) • Planner approach: To obtain feasible and optimal trajectories, optimal control problem solved using pseudospectral methods Albert Caubet

  5. Analytical motions • Biggs, J. D.: Optimal geometric motion planning for spin-stabilized spacecraft • Functional optimization problem with quadratic cost function  Application of Pontryagin’s Minimum Principle  Integrable Hamiltonian system • Angular velocities are trigonometric functions with 3 parameters (plus manoeuver time and/or spin speed) • Pagnozzi & Maclean: Analytical solutions for free motion in quaternion form • Solutions for the axisymmetric and asymmetric case (requires evaluation of Jacobi elliptic functions) • Optimization parameters: initial angular velocities • Fast parametric optimization to meet final position • Analytical solutions usually do not meet real trajectory requirements, e.g. rest-to-rest, pointing constraints, etc Albert Caubet

  6. Pseudospectral methods for O.C. • Optimal Control problem: • Determine u(t), x(t)for a (constrained) dynamic system in order to minimise a performance index • PS methods for OC: • Discretize an optimal control problem to formulatea NLP problem: • Functions approximated using specific collocation points (roots of the time derivative of Legendre poly.) • Differential equations approximated by system of algebraic equations • Cost functional approximated by Gaussian quadrature • Solved numerically to find local optimal solutions • Software used: PSOPT (NLP solver: IPOPT, quasi-newton method) • Characteristics: • Exponential (spectral) rate of convergence • Accurate results with few nodes • Importance of a good initial guess • State of the art: being embedded in UAV for real-time planning Albert Caubet

  7. Some conclusions… • Analytically derived trajectories are (must be) quickly computed • Previous analytically derived trajectories are an initial guess for PSOPT  either the computation time or final optimization cost are improved • Promising approach – effort required to improve the quality of the initial guess, to be closer-to-optimal Albert Caubet

  8. Future work • Short term: • Explore other analytical initial guesses for PS methods – shape-based methods • Try different planning algorithms – RRT*, MPC, only analytical… • Combine actuators: RW + magnetorquers • Mid term • Select and design a suitable planner algorithm • Test robustness with accurate sensors, actuators, disturbances model • Add DOF for translation motions: satellite inspection applications • Long term • Implement and test • Collaboration with Clyde Space • Extrapolation to UAV systems Albert Caubet

  9. Thanks for your attention albert.caubet@strath.ac.uk

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